U.S. patent number 8,170,316 [Application Number 12/243,830] was granted by the patent office on 2012-05-01 for tomographic imaging with a stripe-like shaped sensor.
This patent grant is currently assigned to California Institute of Technology. Invention is credited to Mladen Barbic, Axel Scherer.
United States Patent |
8,170,316 |
Barbic , et al. |
May 1, 2012 |
Tomographic imaging with a stripe-like shaped sensor
Abstract
Tomographic imaging using an imaging sensor that has a
stripe-like shape is disclosed where a stripe sensor is
mechanically scanned over a sample at different angles. For a
single stripe detector imaging, linear motion and angular rotation
are required. Single stripe sensor imaging may be performed using
an elongated inductive coil detector. By utilizing an array of
parallel stripe sensors that can be individually addressed,
two-dimensional imaging can be performed with rotation only,
eliminating the requirement for linear motion, e.g. with parallel
coils array. Imaging with a stripe-type sensor of particular width
and thickness (where width is much larger than thickness) is
resolution limited only by the thickness (smaller parameter) of the
sensor. Multiple sensor families can be produced where this imaging
technique may be beneficial such as magneto-resistive, inductive,
SQUID, and Hall effect sensors, and particularly in the field of
magnetic resonance imaging (MRI).
Inventors: |
Barbic; Mladen (Ashburn,
VA), Scherer; Axel (Laguna Beach, CA) |
Assignee: |
California Institute of
Technology (Pasadena, CA)
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Family
ID: |
40508441 |
Appl.
No.: |
12/243,830 |
Filed: |
October 1, 2008 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20090087064 A1 |
Apr 2, 2009 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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60997140 |
Oct 1, 2007 |
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Current U.S.
Class: |
382/131;
382/132 |
Current CPC
Class: |
G01R
33/345 (20130101); G01R 33/3415 (20130101); A61B
6/504 (20130101); G01R 33/4824 (20130101) |
Current International
Class: |
G06K
9/00 (20060101) |
Field of
Search: |
;382/131-132 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
PCT/US08/78495 International Search Report and Written Opinion.
Feb. 13, 2009. cited by other.
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Primary Examiner: Mehta; Bhavesh
Assistant Examiner: Shah; Utpal
Attorney, Agent or Firm: Canady & Lortz LLP Lortz;
Bradley K.
Government Interests
STATEMENT OF GOVERNMENT RIGHTS
The U.S. Government has certain rights in this invention pursuant
to Grant No. HG026440 awarded by the National Institutes of Health
and Grant No. DMR0349319 & 0622228 awarded by the National
Science Foundation.
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims the benefit under 35 U.S.C. .sctn.119(e) of
the following U.S. provisional patent application, which is
incorporated by reference herein:
U.S. Provisional Patent Application No. 60/997,140, filed Oct. 1,
2007, and entitled "METHOD OF TOMOGRAPHIC IMAGING WITH A
STRIPE-LIKE SHAPED SENSOR", by Barbic et al.
Claims
What is claimed is:
1. An apparatus, comprising: a radiation source for delivering
radiation comprising information of a sample; one or more stripe
sensor elements, each having a width substantially greater than a
thickness, for generating a plurality of one-dimensional projection
scan signals of the sample, each of the one-dimensional projection
scan signals generated from the directed radiation received by the
one or more stripe sensor elements at a distinct relative angle;
and one or more computing devices for deriving a tomographic image
of the sample by combining the plurality of one-dimensional
projection scan signals of the sample.
2. The apparatus of claim 1, wherein deriving the tomographic image
of the sample comprises calculating a Fourier transform of the
plurality of one-dimensional projection scan signals,
multiplication by a ramp function in conjugate space followed by an
inverse transformation, and finally integration over all
angles.
3. The apparatus of claim 1, wherein the received radiation
comprises the information of the sample by reflection from the
radiation source off the sample.
4. The apparatus of claim 1, wherein the received radiation
comprises the information of the sample by transmission from the
radiation source across the sample.
5. The apparatus of claim 1, wherein the received radiation
comprises the information of the sample by emission where the
sample comprises the radiation source itself.
6. The apparatus of claim 1, wherein the one or more stripe sensor
elements are scanned linearly across the sample at each distinct
relative angle to generate each of the plurality of one-dimensional
scan signals of the sample.
7. The apparatus of claim 1, wherein the one or more stripe sensor
elements each provide substantially equal sensitivity along the
width.
8. The apparatus of claim 1, wherein the one or more stripe sensor
elements each comprise an elongated inductive coil loop including
two substantially parallel conductors.
9. The apparatus of claim 1, wherein the one or more stripe sensor
elements are selected from the group comprising thin film
magneto-resistive sensors, asymmetric superconducting interference
devices (SQUIDS), nuclear magnetic resonance (NMR) elongated
micro-fabricated waveguides and stripelines, planar asymmetric
micro-Hall detectors and microwave near-field slit probes.
10. The apparatus of claim 1, wherein the one or more stripe sensor
elements comprises a plurality of adjacent stripe sensor elements
in a linear array each adjacent along the width.
11. The apparatus of claim 10, wherein each of the plurality of the
one-dimensional projection scan signals is generated by
sequentially sensing the plurality of adjacent stripe sensor
elements at the distinct relative angle.
12. The apparatus of claim 10, wherein each of the plurality of
adjacent stripe sensor elements of the linear array comprise an
elongated inductive coil loop including two substantially parallel
conductors and the adjacent stripe sensor elements share a common
conductor of the two substantially parallel conductors.
13. A method, comprising the steps of: directing radiation
comprising information of a sample from a radiation source;
generating a plurality of one-dimensional projection scan signals
of the sample, each of the one-dimensional projection scan signals
generated from the directed radiation received by one or more
stripe sensor elements at a distinct relative angle, each of the
one or more stripe sensor elements having a width substantially
greater than a thickness; and deriving a tomographic image of the
sample by combining the plurality of one-dimensional projection
scan signals of the sample with one or more computing devices.
14. The method of claim 13, wherein deriving the tomographic image
of the sample comprises: calculating a Fourier transform of the
plurality of one-dimensional projection scan signals; multiplying
the Fourier transform by a ramp function in conjugate space;
performing an inverse transformation on the multiplied Fourier
transform; and integrating the inverse transformed multiplied
Fourier transform over all angles.
15. The method of claim 13, wherein directing the radiation
comprises reflecting the radiation from the radiation source off
the sample such that the received radiation comprises the
information of the sample.
16. The method of claim 13, wherein directing the radiation
comprises transmitting the radiation from the radiation source
across the sample such that the received radiation comprises the
information of the sample.
17. The method of claim 13, wherein directing the radiation
comprises emitting the radiation from the sample such that received
radiation from the sample itself comprises the information of the
sample.
18. The method of claim 13, further comprising scanning the one or
more stripe sensor elements linearly across the sample at each
distinct relative angle to generate each of the plurality of
one-dimensional scan signals of the sample.
19. The method of claim 13, wherein the one or more stripe sensor
elements each provide substantially equal sensitivity along the
width.
20. The method of claim 13, wherein the one or more stripe sensor
elements each comprise an elongated inductive coil loop including
two substantially parallel conductors.
21. The method of claim 13, wherein the one or more stripe sensor
elements are selected from the group comprising thin film
magneto-resistive sensors, asymmetric superconducting interference
devices (SQUIDS), nuclear magnetic resonance (NMR) elongated
micro-fabricated waveguides and stripelines, planar asymmetric
micro-Hall detectors and microwave near-field slit probes.
22. The method of claim 13, wherein the one or more stripe sensor
elements comprises a plurality of adjacent stripe sensor elements
in a linear array each adjacent along the width.
23. The method of claim 22, wherein generating the plurality of
one-dimensional projection scan signals of the sample comprises
sequentially sensing each of the plurality of the one-dimensional
projection scan signals from the plurality of adjacent stripe
sensor elements at the distinct relative angle.
24. The method of claim 22, wherein each of the plurality of
adjacent stripe sensor elements of the linear array comprise an
elongated inductive coil loop including two substantially parallel
conductors and the adjacent stripe sensor elements share a common
conductor of the two substantially parallel conductors.
25. An apparatus, comprising: a radiation source means for
directing radiation comprising information of a sample; one or more
stripe sensor element means, each having a width substantially
greater than a thickness, for generating a plurality of
one-dimensional projection scan signals of the sample, each of the
one-dimensional projection scan signals generated from the directed
radiation received by the one or more stripe sensor element means
at a distinct relative angle; and one or more computing device
means for deriving a tomographic image of the sample by combining
the plurality of one-dimensional projection scan signals of the
sample.
26. The apparatus of claim 25, wherein the one or more stripe
sensor element means are scanned linearly across the sample at each
distinct relative angle to generate each of the plurality of
one-dimensional scan signals of the sample.
27. The apparatus of claim 25, wherein the one or more stripe
sensor element means comprise a plurality of adjacent stripe sensor
elements in a linear array each adjacent along the width and each
of the plurality of the one-dimensional projection scan signals is
generated by sequentially sensing the plurality of adjacent stripe
sensor elements at the distinct relative angle.
28. The apparatus of claim 25, wherein deriving the tomographic
image of the sample comprises calculating a Fourier transform of
the plurality of one-dimensional projection scan signals,
multiplication by a ramp function in conjugate space followed by an
inverse transformation, and finally integration over all angles.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to sensors. Particularly, this invention
relates to sensor techniques for tomographic imaging.
2. Description of the Related Art
Imaging of samples through projections has been an important
concept ever since the discovery of x-rays, and has been used in
the gravitational theory and radio astronomy before becoming
widespread through computerized tomography in x-ray, electron, and
optical imaging, among others. See e.g., A. Cormack, J. Appl. Phys.
34, 2722 (1963); G. Hounsfield, British J. Radiol. 46, 1016 (1973);
D. J. de Rosier arid A. Klug, Nature (London) 217 130 (1968); and
D. E. Kuhl and R. Q. Edwards, Radiol. 80, 653 (1963). The first
report of magnetic resonance imaging (MRI) had its roots in image
reconstruction from projections. See, P. C. Lauterbur, Nature
(London) 242, 190 (1973). Computerized tomographic image
reconstruction algorithms for conventional radiation-based
tomography are by now well developed and can be easily transferred
to novel imaging methodologies such as the one described in this
disclosure on stripe sensor tomography. See e.g, G. T. Herman,
Image Reconstruction from Projections, Academic Press, New York
(1980); F. Natterer, The Mathematics of Computerized Tomography,
John Wiley & Sons, New York (1986); A. C. Kak and M. Slaney,
Principles of Computerized Tomographic Imaging SIAM, Philadelphia
(2001); S. R. Deans, Tile Radon Transform and Some of Its
Applications, Krieger Publishing Company, Malabar (1993); and P. T.
Callaghan, Principles of Nuclear Magnetic Resonance Microscopy,
Oxford University Press. New York (1991), which are incorporated by
reference herein.
The various disciplines of scanning probe microscopy conventionally
employ a point-by-point raster scanning of the sample in the x-y
plane as a common way of obtaining a two-dimensional image of the
sample. However, it can frequently be the case that the scanning
sensor is not of the point type, but is instead of the stripe
shape, typically due to the thin-film lithographic character of
sensor fabrication. For example, in scanning magneto-resistance
microscopy the imaging sensor is a thin film magneto-resistive
element of small thickness, t, and much larger width, w. See, S Y.
Yamamoto and S. Schultz. Appl. Phys. Lett. 69, 3263 (1996). By
raster scanning of this sensor in the x-y plane, a two-dimensional
image of a magnetic sample can be obtained. See also, S. Y.
Yamamoto, R. O'Barr, S. Schultz, and A. Scherer, IEEE Trans. Magn.
33, 1016 (1997); M. Todorovic, S. Schultz, J. Wong, and A. Scherer,
Appl. Phys. Lett. 74, 2516 (1999); and M. Barbic, S. Schultz, J.
Wong, and A. Scherer, IEEE Trans. Magn. 37, 1657 (2001). There has
been a perceived notion in such reports that two-dimensional images
obtained with a stripe-type magneto-resistive sensor are limited in
spatial resolution by thickness, t, in the x-direction, and width,
w, in the y-direction.
In view of the foregoing, there is a need in the art for
apparatuses and methods for more efficient apparatuses and methods
for tomographic imaging, e.g. using stripe-like sensors. In
addition, there is a need for such apparatuses and methods that can
deliver high spatial resolution with reduced scanning requirements.
There is further a need for such imaging apparatuses and methods
that can operate more quickly and efficiently than conventional
techniques. These and other needs are met by the present invention
as detailed hereafter.
SUMMARY OF THE INVENTION
Tomographic imaging for the case of an imaging sensor that has a
stripe-like shape is disclosed. Surprisingly, there is a common
analytical principle between two-dimensional tomography using
conventional electromagnetic or particle radiation and tomography
where a stripe sensor is mechanically scanned over a sample at
different angles. For a single stripe detector imaging, linear
motion and angular rotation are required. Single stripe sensor
imaging may be performed using an elongated inductive coil
detector. By utilizing an array of parallel stripe sensors that can
be individually addressed, two-dimensional imaging can be performed
with rotation only, eliminating the requirement for linear motion,
e.g. with parallel coils array. Imaging with a stripe-type sensor
of particular width and thickness (where the width is much larger
than the thickness) is resolution limited only by the thickness
(smaller parameter) of the sensor. Multiple sensor families can be
produced where this imaging technique may be beneficial such as
magneto-resistive, inductive, SQUID, and Hall effect sensors, and
particularly in the field of Magnetic Resonance Imaging.
A typical apparatus embodiment of the invention comprises a
radiation source for directing radiation comprising information of
a sample, one or more stripe sensor elements, each having a width
substantially greater than a thickness, for generating a plurality
of one-dimensional projection scan signals of the sample, each of
the one-dimensional projection scan signals generated from the
directed radiation received by the one or more stripe sensor
elements at a distinct relative angle, and one or more computing
devices for deriving a tomographic image of the sample by combining
the plurality of one-dimensional projection scan signals of the
sample. Deriving the tomographic image of the sample may comprise
calculating a Fourier transform of the plurality of one-dimensional
projection scan signals, multiplication by a ramp function in
conjugate space followed by an inverse transformation, and finally
integration over all angles. Typically, the one or more stripe
sensor elements each provide substantially equal sensitivity along
the width. The received radiation may comprise information of the
sample by reflection from the radiation source off the sample, by
transmission from the radiation source across the sample, or by
emission where the sample comprises the radiation source
itself.
Embodiments of the invention may be implemented with stripe sensor
elements of various types. For example, the one or more stripe
sensor elements may be thin film magneto-resistive sensors,
asymmetric superconducting interference devices (SQUIDS), nuclear
magnetic resonance (NMR) elongated micro-fabricated waveguides and
stripelines, planar asymmetric micro-Hall detectors or microwave
near-field slit probes. In one exemplary embodiment of the
invention, the one or more stripe sensor elements each comprise an
elongated inductive coil loop including two substantially parallel
conductors.
In some embodiments of the invention, the one or more stripe sensor
elements are scanned linearly across the sample at each distinct
relative angle to generate each of the plurality of one-dimensional
scan signals of the sample. In some embodiments of the invention,
the one or more stripe sensor elements may comprise a plurality of
adjacent stripe sensor elements in a linear array each adjacent
along the width. Each of the plurality of the one-dimensional
projection scan signals may be generated by sequentially sensing
the plurality of adjacent stripe sensor elements at the distinct
relative angle. (This can eliminate the need to linearly scan the
one or more stripe sensor element across the sample.) In one
notable example, each of the plurality of adjacent stripe sensor
elements of the linear array may comprise an elongated inductive
coil loop including two substantially parallel conductors and the
adjacent stripe sensor elements share a common conductor of the two
substantially parallel conductors.
A typical method embodiment of the invention may comprise the steps
of directing radiation comprising information of a sample from a
radiation source, generating a plurality of one-dimensional
projection scan signals of the sample, each of the one-dimensional
projection scan signals generated from the directed radiation
received by one or more stripe sensor elements at a distinct
relative angle, each of the one or more stripe sensor elements
having a width substantially greater than a thickness, and deriving
a tomographic image of the sample by combining the plurality of
one-dimensional projection scan signals of the sample with one or
more computing devices. Deriving the tomographic image of the
sample may comprises the steps of calculating a Fourier transform
of the plurality of one-dimensional projection scan signals,
multiplying the Fourier transform by a ramp function in conjugate
space, performing an inverse transformation on the multiplied
Fourier transform, and integrating the inverse transformed
multiplied Fourier transform over all angles. Method embodiments of
the invention may be further modified consistent with the
apparatuses and systems described herein.
For example, directing the radiation may comprise reflecting the
radiation from the radiation source off the sample such that the
received radiation comprises the information of the sample.
Alternately, the radiation may be transmitted from the radiation
source across the sample such that the received radiation comprises
the information of the sample. The radiation may also be emitted
from the sample such that received radiation from the sample itself
comprises the information of the sample.
BRIEF DESCRIPTION OF THE DRAWINGS
Referring now to the drawings in which like reference numbers
represent corresponding parts throughout:
FIG. 1A illustrates a convention computerized tomographic imaging
technique;
FIG. 1B illustrates a novel stripe sensor computerized tomographic
imaging technique;
FIG. 1C is a schematic diagram of an exemplary tomographic imager
embodiment of the invention;
FIG. 1D illustrates a generalized transmission, reflection and
emission configuration for an embodiment of the invention using a
stripe sensor element;
FIG. 2A is an example embodiment of the invention employing an
elongated inductive coil loop;
FIG. 2B illustrates the test sample for the elongated inductive
coil loop embodiment of the invention;
FIG. 3A shows a plot of three line scans representing
one-dimensional projections of a two-dimensional sample from an
example embodiment of the invention;
FIG. 3B is a two-dimensional image of the sample from an example
embodiment of the invention;
FIG. 4A illustrates and example apparatus for tomographic imaging
employing an array of stripe sensor elements;
FIG. 4B illustrates an example embodiment of the invention
comprising a stripe sensor array of inductive sensor elements;
FIG. 5A illustrates an example embodiment of a sensor array
prepared with conventional optical lithography techniques;
FIG. 5B shows a resulting image, reconstructed using the applied
algorithm of Equation (2) employing the sensor array of FIG.
5A;
FIG. 6A illustrates an example conventional point-by-point
rastering imaging process;
FIG. 6B shows the difference between the sensor sensitivity for an
example inductive stripe sensor element and a point sensor element
as a function of the sample distance along the z axis
(perpendicular to the sample surface);
FIG. 7 illustrates a nanofabricated version of an example inductive
loop sensor array in accordance with an embodiment of the
invention;
FIG. 8A is a flowchart of an exemplary method of tomographic
imaging; and
FIG. 8B is a flowchart of a sub-method for deriving the tomographic
image by combining the plurality of one-dimensional projection scan
signals of the sample.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
1. Overview
Embodiments of the present improve over the various conventional
disciplines of scanning probe microscopy where a point-by-point
raster scanning of the sample in the x-y plane is a common way of
obtaining a two-dimensional image of the sample. Embodiments of the
present invention recognize that it can frequently be the case for
such techniques that the scanning sensor may be not of the point
type, but having a stripe shape, typically due to the thin film
lithographic character of many sensor fabrication techniques. For
example, in the scanning magnetoresistance microscopy, the imaging
sensor is a thin film magnetoresistive element of small thickness t
and much larger width w. By raster scanning of this sensor in the
x-y plane, a two-dimensional image of a magnetic sample can be
obtained. There has been a perceived notion in those reports that
two-dimensional images obtained with a stripe-type magnetoresistive
sensor are limited in spatial resolution by thickness t in the x
direction, and width w in the y direction. It is an object of the
present disclosure to show that by linear scanning motion of the
stripe-type sensor at different angular orientations combined with
the tomographic imaging principles, two-dimensional images of
samples can be obtained that are limited in spatial resolution
along both x and y axes by only the thickness t, i.e., the smaller
parameter of the sensor. See, S. Y. Yamamoto and S. Schultz, Appl.
Phys. Lett. 69, 3263 1996; S. Y. Yamamoto, R. O'Barr, S. Schultz,
and A. Scherer, IEEE Trans. Magn. 33, 3016 1997; M. Todorovic, S.
Schultz, J. Wong, and A. Scherer, Appl. Phys. Lett. 74, 2516 1999;
and M. Barbic, S. Schultz, J. Wong, and A. Scherer, IEEE Trans.
Magn. 37, 1657 2001, which are incorporated by reference
herein.
Some embodiments of the invention may employ linear scanning motion
of one or more stripe-type sensor elements at different angular
orientations to generate multiple one-dimensional projections that
are combined with tomographic imaging principles to yield a
two-dimensional image of a sample that are limited in spatial
resolution along both x- and y-axes by only the thickness, t, i.e.
the smaller parameter, of the sensor. Other embodiments of the
invention may forego linear scanning through implementation of an
array of stripe sensor elements where each one-dimensional
projection is generated by sequentially sensing each stripe sensor
element of the array. Stripe sensor element techniques described
herein may be applied across a range of sensor types, provided they
are amenable to a stripe-like configuration exhibiting a
substantially uniform sensitivity response along the width of the
sensor.
2. Single Stripe Sensor Imaging
FIGS. 1A & 1B illustrate conventional radiation-based
two-dimensional tomography and tomography where a stripe sensor is
mechanically scanned over a sample at a sequence of different
angles. FIG. 1A shows the schematic representation of a
conventional tomography configuration for imaging a sample 100 with
the parameters used in the image reconstruction process indicated.
Radiation 102A, 102B comprising uniformly separated parallel rays
(electromagnetic or particle) from a radiation source (not shown)
is used to obtain an image projection 106A, 106B along an axis at a
detector 104A, 104B (indicated by the position of the q axis) on
the opposite side of the radiation source at different angles,
.phi.. For each projection 106A, 106B, a one-dimensional Radon
transform of the sample density function .rho.(x, y) is formed:
.PHI..function..intg..PHI..times..times..rho..function..times.d
##EQU00001## By obtaining multiple one-dimensional Radon transforms
106A, 106B from Equation (1) at the different angles, .phi., image
reconstruction is performed by the Fourier transform filtered
back-projection algorithm for parallel projections:
.function..intg..pi..times..intg..infin..infin..times..intg..infin..infin-
..times..PHI..function.eI.times..times..times..pi..times..times..times.d.t-
imes..times.eI.pi..times..times..times.d.times.d.PHI. ##EQU00002##
See A. C. Kak and M. Slaney, "Principles of Computerized
Tomographic Imaging SIAM, Philadelphia (2001), which is
incorporated by reference herein. This reconstruction process
involves calculation of the Fourier transform of the Radon
transform (the inner-most bracketed term), multiplication by a ramp
function |k| in conjugate space followed by an inverse
transformation (outer bracketed term), and finally integration over
all angles for the completion of the image reconstruction
(outermost integration term). Note that the detector 104A, 104B may
be repositioned to the different angles, .phi. or multiple
detectors 104A, 104B may be used.
FIG. 1B is schematic diagram showing operation of stripe sensor
tomography in accordance with an embodiment of the invention. In
this case, a linear stripe sensor element 120 of width, w, and
thickness, t, (having the width substantially greater than the
thickness) is mechanically scanned over a sample 122 that extends
over a region that is smaller than the width of the stripe sensor
element 120. (Note that the overall sample 122 may actually be
larger than the width of the stripe sensor element 120, but the
scanned portion of the sample 122 will be limited to the width of
the stripe sensor element 120.) Typically, the stripe sensor
element 120 may have equal sensitivity along its width, w, (as is
assumed in this description), and each single line scan of the
stripe sensor element 120 will result in the one-dimensional data
that represents a one-dimensional projection of the two-dimensional
sample. By scanning the stripe sensor element 120 across the sample
122 at different angles .phi. 124 as shown in FIG. 1B (or
equivalently by rotating the sample 122 to the line at various
angles .phi. and scanning the stripe sensor element 120 along the
same line) multiple one-dimensional projections of the
two-dimensional sample represented by Equation (1) are obtained and
may be stored as will be understood by those skilled in the art.
Finally, by utilizing the reconstruction process of Equation (2) on
the stored multiple one-dimensional projections, which may be
implemented with one or more computing devices (e.g., a programmed
computer or dedicated hardware computing device), a two-dimensional
tomographic image of the sample can be generated as further
described with respect to FIGS. 3A & 3B. Note that although
only two one-dimensional projection scans are illustrated in FIG.
1B (separate by the angle .phi.), additional one-dimensional
projection scans at other distinct relative angles applied in the
algorithm of Equation (2) will improve the imaging results.
FIG. 1C is a schematic diagram of an exemplary tomographic imager
embodiment of the invention. The imager 140 comprises a radiation
source 146 for emitting radiation 154 across a sample 142. The
stripe sensor element 144 has a width substantially greater than
its thickness and is used to generate a plurality of
one-dimensional projection scan signals 148 of the sample 142. Each
of the one-dimensional projection scan signals 148 is generated
from the radiation received by the stripe sensor element 144 as the
sensor element 144 is linearly scanned over the sample 142 from
first to a second position 158 in the direction of the indicated
arrow.
As shown in FIG. 1C, the radiation source 146 emits radiation 154
across a sample 142 to be received by the stripe sensor element
144. However, those skilled in the art will appreciate that it is
only necessary that radiation 154 that comprises information of the
sample 142 is directed to be received by the stripe sensor element
144. The type and definition of the applied radiation 154, e.g.,
particle or electromagnetic, power, wavelength, etc., will vary
depending upon the particular application as will be understood by
those skilled in the art. Embodiments of the invention may be
implemented in different configurations are possible including a
transmission, reflection, and emission configuration. FIG. 1C
illustrates another example of a transmission configuration where a
separate radiation source 154 emits radiation 154 across a sample
142 to impart information of the sample 142 to the radiation 154.
(Note that the radiation source 154 is shown on one side of the
stripe sensor element 144 in FIG. 1C, however, the radiation source
will typically be disposed behind the sample 142 in a typical
transmission configuration as described below in FIG. 1D.)
Each of the additional one-dimensional projection scan signals 148
is generated at a distinct relative angle. This may be accomplished
by repositioning the stripe sensor element 144 (and possibly the
radiation source 146) relative to sample 142 (e.g., as shown by the
second position 156 for the stripe sensor element 144 and radition
source 146 in phantom which would yield a second one-dimensional
projection scan signal). Alternately, the sample 142 may be
repositioned relative to the stripe sensor element 144 (and
possibly the radiation source 146). In any case, each
one-dimensional projection scan signal (e.g., scans signals 1 to N)
148 corresponds to a linear scan made at a distinct relative angle.
The plurality of one-dimensional projection scan signals 148 are
processed to derive the tomographic image 152 of the sample
142.
The plurality of one-dimensional projection scan signals 148 are
provided to one or more computing devices 150, which apply the
algorithm previously described and combine the plurality of
one-dimensional projection scan signals 148 to derive a tomographic
image 152 of the sample 142. Any suitable computing device 150,
e.g., a programmed computer or dedicated hardware computing device,
may be used to drive the sensor element and/or process the
plurality of one-dimensional projection scan signals 148 to derive
a tomographic image 152 as will be understood by those skilled in
the art. Thus, the one or more computing devices 150 calculate a
Fourier transform of the plurality of one-dimensional projection
scan signals 148, multiply this by a ramp function in conjugate
space, perform an inverse transformation, and finally integrate
over all angles.
FIG. 1D illustrates generalized reflection, transmission, and
emission configurations 160, 162, 164, for an embodiment of the
invention using a stripe sensor element 144. In a reflection
configuration 160, the radiation source 146 is substantially
co-located with the stripe sensor element 144 (i.e., on the same
side of the sample 142). In this case, information of the sample
142 is imparted to the radiation 154 as a consequence of it being
reflected off the sample 142 and back to the stripe sensor element
142. In a transmission configuration 162, information of the sample
142 is imparted to the radiation 154 as emitted from the source 146
across the sample 142 to the stripe sensor element, e.g., on the
opposite side of the sample. Finally, in an emission configuration
164 the sample 142 itself is also the radiation source 146.
Radiation 154 emitted from the sample 142 surface inherently
comprises information of the sample 142.
The inventive principle is common in each of the example
configurations 160, 162, 164 as will be understood by those skilled
in the art. Each employs a stripe sensor element 144 to generate a
plurality of one-dimensional projection scan signals of the sample
from the directed radiation received by the stripe sensor element
144 (each at a distinct relative angle). As illustrated, the
one-dimensional projection scan signals are generated as the stripe
sensor element 144 is linearly scanned from the first position to
the second position 158. In each configuration 160, 162, 164, the
received radiation 154 comprises information of the sample 142,
although the information may be acquired through different
processes, reflection off the sample, transmission through the
sample, or emission from the sample. Each of the described
configurations 160, 162, 164, may employ one or more computing
devices to derive a tomographic image of the sample operating in
the same manner as the imager 140 of FIG. 1B. As previously
mentioned, the particular radiation and sensor types, as well as
the specific parameters of the configuration will depend upon the
particular application, as will be understood by those skilled in
the art.
The imaging apparatus in accordance with an embodiment of the
invention in any configuration may employ a range of sensor element
types. For example, the stripe sensor element may comprise an
elongated inductive coil loop including two substantially parallel
conductors as will be described in detail hereafter. Those skilled
in the art will appreciate that analogous imaging systems may be
readily developed for other sensor elements applying the described
principles including thin film magneto-resistive sensors,
asymmetric superconducting interference devices (SQUIDS), nuclear
magnetic resonance (NMR) elongated micro-fabricated waveguides and
stripelines, planar asymmetric micro-Hall detectors and microwave
near-field slit probes. The particular type of the radiation source
146 and arrangement with the sensor element 144 will depend upon
the specific application.
A example tomographic imaging apparatus embodiment of the invention
may include a stripe sensor element that comprises an elongated
inductive coil loop detector, shown in FIG. 2A. This example
structure provides simplicity and has potential use in single sided
magnetic resonance imaging or eddy current non-destructive
evaluation as will be understood by those skilled in the art. See,
e.g., B. Blumich, "NMR Imaging of Materials," Oxford University
Press, New York (2000), which is incorporated by reference herein.
The example coil may be made from two parallel conductors inserted
into capillary tubes for insulation and disposed having a uniform
separation of t=750 .mu.m. The loop may be mounted on a linear
mechanical translation stage with the axis of the linear motion
indicated by the arrowed line in FIG. 2A. The tested "sample" to be
scanned for imaging may comprise a circular coil pair, each
approximately 1.5 mm in diameter, representing two point sources
separated by a distance slightly larger than the thickness, t, of
the sensor but much smaller than the width, w, of the sensor. The
sample is mounted on the mechanical rotation stage visible in the
figure. The magnified view of the two loop sources and the two
conductors of the inductive stripe-like coil detector are shown in
FIG. 2B. The sources may be driven in phase with an approximately
100 mA AC electric current electrical signal at approximately 11
kHz from an audio power amplifier (e.g., Teach Spin Model PAA1-A)
driven by a lock-in amplifier signal source (e.g., Stanford
Research Systems Model SR830). Due to the low output impedance of
the stripe coil sensor, the detected signal may be coupled to a
low-noise transformer pre-amplifier (Stanford Research Systems
Model SR554) followed by the signal input channel of the lock-in
amplifier. The loop may be scanned in 250 .mu.m steps at 500 .mu.m
height above the sample surface. The rotation stage may be rotated
by approximately 10 degrees after each linear scan.
FIG. 3A shows three one-dimensional projection scans (of 18 total
in this example) representing three different one-dimensional
projections of a two-dimensional sample at different angular
orientations. At zero degrees, the two sources are clearly resolved
as indicated in graph, and at 90 degrees only a single large peak
is detected, as expected for two in-phase AC sources concurrently
under the detector.
FIG. 3B shows the resulting two-dimensional image of the sample
(from 18 example projections) using the formalism of tomographic
filtered back-projection image reconstruction of Equation (2)
applied as described above. The two sources are clearly resolved,
and the main argument that the two-dimensional image resolution is
limited in both directions by only the narrow thickness parameter
of the sensor is demonstrated.
It should be noted that a unique feature of this technique, as
related to potential use in MRI, is that the imaging may be
performed without the need for external high power gradient
magnetic fields typically employed in MRI. In the stripe sensor
case, the imaging resolution would be determined by the sensor
thickness, and not by the gradient field values that could be
achieved from external current carrying conductors.
3. Stripe Sensor Element Array Imaging
FIG. 4A illustrates an example imager apparatus 400 for tomographic
imaging employing an array 416 of stripe sensor elements 404A-404K.
Here, the principle of stripe-type sensor two-dimensional
tomography previously described is further extended to
two-dimensional imaging using a sensor array 416. This imager 400
generally operates in the same manner as the imager 140 of FIG. 1C.
Thus, the imager 400 comprises a radiation source 406 for emitting
radiation 416 across a sample 402. The type and definition of the
applied radiation 418, e.g., particle or electromagnetic, power,
wavelength, etc., will vary depending upon the particular
application as will be understood by those skilled in the art.
The stripe sensor array 416 in this imager 400 comprises a
plurality of stripe sensor elements 404A-404K. Each has a width
substantially greater than its thickness. In this case, the
plurality of one-dimensional projection scan signals 408 of the
sample 402 are generated by sequentially sensing the plurality of
stripe sensor elements 404A-404K. Each of the one-dimensional
projection scan signals 408 is generated from the radiation emitted
across the sample and received by the array 416 as the plurality of
stripe sensor elements 404A-404K are sequentially sensed.
Here also, each of the additional one-dimensional projection scan
signals 408 is generated at a distinct relative angle. This may be
accomplished by repositioning the stripe sensor array 416 (and
possibly the radiation source 406) relative to sample 402 (e.g., as
shown by the second position 414 for the stripe sensor array 416
and radition source 406 in phantom which yields a second
one-dimensional projection scan signal). Alternately, the sample
402 may be repositioned relative to the stripe sensor array 416
(and possibly the radiation source 406). In any case, each
one-dimensional projection scan signal (e.g., scans signals 1 to N)
408 corresponds to sequential sensing of the elements 404A-404K of
the array 416 made at a distinct relative angle. The plurality of
one-dimensional projection scan signals 408 are processed to derive
the tomographic image 412 of the sample 402 in the same manner as
those of the imager 140 of FIG. 1C.
The plurality of one-dimensional projection scan signals 408 are
provided to one or more computing devices 410, which apply the
algorithm previously described and combine the plurality of
one-dimensional projection scan signals 408 to derive a tomographic
image 412 of the sample 402. Any suitable computing device 410,
e.g., a programmed computer or dedicated hardware computing device,
may be used to drive the sensor element and/or process the
plurality of one-dimensional projection scan signals 408 to derive
a tomographic image 412 as will be understood by those skilled in
the art. Thus, the one or more computing devices 410 calculate a
Fourier transform of the plurality of one-dimensional projection
scan signals 408, multiply this by a ramp function in conjugate
space, perform an inverse transformation, and finally integrate
over all angles.
Embodiments of the invention employing a stripe sensor element
array may also be implemented in any of the configurations 160,
162, 164, reflection, transmission, and emission, previously
described in FIG. 1D. In each configuration 160, 162, 164, the
single stripe sensor element 144 is replaced with an array spanning
the distance from the first position of the element 144 to the
second position 158 as described in FIG. 4A. The common inventive
principle of each of the example configurations 160, 162, 164 is
applicable to the stripe sensor array as well as will be understood
by those skilled in the art. Each can employ a stripe sensor array
to generate a plurality of one-dimensional projection scan signals
of the sample from the directed radiation received by the stripe
sensor array from sequential sensing of the elements (each scan
taken at a distinct relative angle). The received radiation 154
comprises information of the sample 142 in every configuration 160,
162, 164, although the information may be acquired through
different processes, reflection off the sample, transmission
through the sample, or emission from the sample. Each of the
described configurations 160, 162, 164, may employ one or more
computing devices to derive a tomographic image of the sample
operating in the same manner as the imagers 140, 400 of FIGS. 1B
and 4A. As previously mentioned, the particular radiation and
sensor types, as well as the specific parameters of the
configuration will depend upon the particular application, as will
be understood by those skilled in the art.
The imaging apparatus using a stripe sensor array in any
configuration may employ a range of sensor element types. For
example, the stripe sensor element may comprise an elongated
inductive coil loop including two substantially parallel conductors
as will be described in detail hereafter. Those skilled in the art
will appreciate that analogous imaging systems may be readily
developed for other sensor elements applying the described
principles including thin film magneto-resistive sensors,
asymmetric superconducting interference devices (SQUIDS), nuclear
magnetic resonance (NMR) elongated micro-fabricated waveguides and
stripelines, planar asymmetric micro-Hall detectors and microwave
near-field slit probes. The particular type of the radiation source
406 and arrangement with the sensor elements 404A-404K in the array
416 will depend upon the specific application.
FIG. 4B illustrates an example embodiment of the invention
comprising a stripe sensor array 420 of inductive sensor elements
422A-422H. In this example, the technique as diagrammatically
described in FIG. 4B, employs the example stripe sensor element of
the stripe-type inductive detector loops as the elements 422A-422H
which are sensed by voltages V1-V8, respectively. By creating a
meander-like loop array disposed over a sample 424, and
sequentially detecting voltages at nodes in the array as shown in
FIG. 4B, sensing signals are obtained. As previously mentioned,
employing a sequentially sensed array of stripe sensor elements in
this manners eliminates the requirement for linear translation of
the sample or the sensor element array as would be required with a
single stripe sensor element. One notable advantage of the
inductive sensor element array, e.g. constructed as shown in the
FIG. 4B, is that each single conductor in the array (that has
adjacent conductors on both sides) is used in two detector loops.
For example, the second wire from the bottom in the FIG. 4B is part
of the loop sensing V1 and part of the loop sensing V2. This
arrangement minimizes the number of wires required in the array,
improves the imaging resolution, simplifies the setup, and
potentially reduces the imaging time as well. Each one-dimensional
projection scan signal is generated by sequentially sensing the V1
to V8 at a distinct angle relative to the sample 424 to be imaged.
Processing of the one-dimensional projection scan signals generated
from the array 420 may be performed in the same manner as the
apparatus 400 of FIG. 4A as will be understood by those skilled in
the art.
FIG. 5A illustrates an example embodiment of a sensor array
prepared with conventional optical lithography techniques. The
array comprises 50 Cr/Au wires approximately 50 .mu.m wide, 100 nm
thick, and separated by a center-to-center distance of 400 .mu.m on
a glass substrate for fifty detection loops. Wider wires may be
used to connect the individual sensor elements of the array and fan
out for easy contact access. An example sample is a two point
circular coil pair mounted on a rotation stage (similar to the
prior single stripe sensor element example), electrically arranged
so that the ac currents in them are 180.degree. out of phase. The
data are collected sequentially from each loop of the array using
the same source/audio power amplifier and transformer
preamplifier/lock-in amplifier arrangement, but this time without
any linear translation. After all the loop voltage signals are
recorded in sequence for a single angle, the sample is rotated by
10.degree., and procedure repeated.
FIG. 5B shows a resulting image, reconstructed using the algorithm
of Equation (2) employing the sensor array of FIG. 5A. Again, the
test image is demonstrated by imaging of the two point sources with
two-dimensional resolution limited only by the narrower thickness
parameter of the sensor.
4. Stripe Sensor Versus Point Sensor Raster Imaging
FIG. 6A illustrates an example conventional point-by-point
rastering imaging process. In this section, some of the differences
and consequences of stripe-type sensor imaging, e.g. as shown in
FIG. 1B, compared to a conventional raster scanning point probe
imaging, e.g., as shown in FIG. 6A, to better illustrate features
of embodiments of the invention. Although both imaging
methodologies, the raster scanning point-by-point imaging and
stripe sensor imaging, provide two-dimensional images with
resolution limited by the smaller parameter of the sensor, i.e.,
the thickness of the stripe sensor and size of the point sensor,
respectively, there are several differences. Those skilled in the
art will appreciate that although an inductive pickup loop detector
is discussed in this example, similar analysis may be applied to
other analogous sensor types.
One distinction is in the measurement time and consequently the
signal-to-noise ratio of the two methodologies. In the raster
scanning point probe method of FIG. 6A, the point probe 600
measures and resolves each pixel of the image individually for a
certain measurement time T and only once during the course of the
N.times.N step imaging sequence, e.g. along the dotted path. In
contrast, for the stripe sensor element imaging mode, e.g. of FIG.
1B, the sensor detects multiple pixels of the image for a certain
measurement time T at each step of the N steps linear scan and does
not resolve the pixels along the sensor width. Nevertheless,
through M angular orientations of the linear scans, as previously
described, it still obtains the two-dimensional imaging with
resolution defined by the thickness of the sensor only.
However, note that each pixel of the image in the stripe sensor
element imaging technique may be detected by the sensor for every
angular orientation of the linear scan, and is therefore detected M
times. How this affects the signal to noise ratio (SNR) may be
difficult to precisely estimate, although M times more measurements
of each image pixel in the stripe sensor technique should provide
the square root of M times better SNR. However, the larger length
of the striped-shaped inductive loop sensor results in the larger
sensor resistance R, and therefore larger RMS noise of the sensor
which scales as the square root of R.
There is also a slight difference in the depth of view between the
two imaging modalities (raster point scanning versus stripe element
scanning) for the case of an inductive sensor. Using the principle
of reciprocity, often used in the theory and practice of magnetic
resonance and magnetic recording for signal reception analysis, the
field patterns of the two methods may be compared to estimate the
relative z-axis dependence of sensitivity between the two sensor
shapes. See, e.g., W. F. Brown, Jr., Magnetostatic Principles in
Ferromagnetism, North-Holland, Amsterdam, 1962; D. I. Hoult and R.
E. Richards, J. Magn. Reson. 24, 71 1976; D. I. Hoult and P. C.
Lauterbur, J. Magn. Reson. 34, 425 1979; and S. X. Wang and A. M.
Taratorin, Magnetic Information Storage Technology Academic, San
Diego, 1999, which are incorporated by reference herein.
FIG. 6B shows the difference between the sensor sensitivity for an
example inductive stripe sensor element and a point sensor element
as a function of the sample distance along the z axis
(perpendicular to the sample surface). For the inductive stripe
sensor element example with wires of the stripe loop separated by
distance 2a as compared to the circular loop of radius a, the graph
indicates that the circular loop is more sensitive for the region
of the sample close to the sensor, while the stripe loop is more
sensitive for the region of the sample that is further away from
the sensor. Therefore, the stripe sensor has a larger "depth of
view" and weaker depth dependence of the received signal, while the
point sensor is more sensitive at the surface of the sample and has
steeper depth dependence of reception. The crossover point for
sensitivity is at z=1.21a.
It should also be noted that, as related to potential use in MRI, a
vertical field gradient could be employed for extending the imaging
process to three dimensions. However, the signal from spins that
are over a given stripe detector in the array start to
significantly contribute to the signals being detected by
neighboring stripe detectors. Therefore, spatial resolution may
suffer further away from the detector array.
A comparison can also be made between the N-stripe array sensor
described in FIGS. 4 and 5 and the N.times.N point sensors array
used, for example, in the detection of biomedically related
magnetic fields. See, The SQUID Handbook, edited by J. Clarke and
A. I. Braginski, Wiley-VCH, Berlin, 2006, which is incorporated by
reference herein. Again, both methods, in principle, achieve
similar two-dimensional spatial imaging resolution. The stripe
sensor array needs N times fewer sensors but requires sample (or
array) rotation and tomographic computer reconstruction, while the
N.times.N point sensor array does not require mechanical motion,
but requires N times more detection channels for two-dimensional
image acquisition.
There are two additional challenges that are present in the stripe
sensor tomography described. Flat surface of the sample is one
major restriction. This limitation is typically not an issue in
point sensor scanning probe microscopy, where surface topography is
obtained along with any other parameter of the sample
(electrostatic, magnetic, etc.). Additionally, stripe sensor
element tomography requires substantial uniformity of the sensor
sensitivity response along the width of the sensor. This is well
satisfied for the example inductive stripe sensor element
presented, but implementation may be more problematic in, for
example, a magnetoresistive stripe sensor element, where slight
variation in the point sensitivity function along the sensor length
has been experimentally observed. See, G. A. Gibson, S. Schultz, T.
Carr, and T. Jagielinski, IEEE Trans. Magn., 28, 2310, 1992; and M.
Todorovic and S. Schultz, J. Appl. Phys. 83, 6229, 1998, which are
incorporated by reference herein.
5. Stripe Sensor Element Tomographic Imaging Applications
As previously mentioned, there are many other sensor families that
may be suitable for stripe sensor tomographic implementation as
will be understood by those skilled in the art. For example, thin
film magneto-resistive sensors, asymmetric superconducting quantum
interference devices (SQUIDs), elongated microfabricated waveguides
and striplines, and nanoparticle-tape-filled microcoils used in NMR
detection, planar asymmetric micro-Hall detectors, and microwave
near-field slit probes as suitable candidates. Another possibility
is the extension of the stripe array sensor idea into the submicron
MRI resolution regime. See, M. Todorovic and S. Schultz, J. Appl.
Phys. 83, 6229, 1998; S.-J. Kim, J. Chen, K. Nakajima, T.
Yamashita, S. Takahashi, and T. Hatano, J. Appl. Phys. 91, 8495,
2002; Y. Maguire, I. L. Chuang, S. Zhang, and N. Gershenfeld, Proc.
Natl. Acad. Sci. U.S.A. 104, 9198, 2007; P. J. M. van Bentum, J. W.
G. Janssen, A. P. M. Kentgens, J. Bart and J. G. E. Gardeniers, J.
Magn. Reson. 189, 104, 2007; M. Barbic and A. Scherer, Solid State
Nucl. Magn. Reson. 28, 91, 2005; H. Guillou, A. D. Kent, G. W.
Stupian, and M. S. Leung, J. Appl. Phys., 93, 2746, 2003; F.
Sakran, A. Copty, M. Golosovsky, N. Bontemps, D. Davidov, and A.
Frankel, Appl. Phys. Lett. 82, 1479, 2003; and F. Sakran, A. Copty,
M. Golosovsky, D. Davidov, and P. Monod, Appl. Phys. Lett. 84,
4499, 2004, which are incorporated by reference herein.
FIG. 7 illustrates a nanofabricated version of an example inductive
loop sensor array. In this regime, the flatness of the sample and
the requirement for angular rotation of the sample may prove
especially difficult. However, electro-rotation of samples may
provide one viable solution to the nanoscale angular orientation
challenge as will be understood by those skilled in the art.
Although such miniaturized conductor structures exhibit increased
resistance and therefore may degrade SNR of an inductive detector,
they also provide a higher field per unit current, B.sub.1/I, at
the sample location. Careful and extensive analysis of SNR of
microcoil structures in NMR detection indicates that SNR per unit
volume increases as the inductive detector decreases in size,
further motivating size reduction of the inductive stripe sensor
array. It is also interesting that in potential magnetic resonance
imaging implementation on this size scale, the technique would
operate in the regime where nuclear spin noise signal is
appreciable and comparable to the conventional NMR signal.
Therefore, two-dimensional imaging with a submicron stripe sensor
array in that case may be performed without the need for external
imaging gradient fields and without the need for high power
radio-frequency excitation. See, W. M. Arnold and U. Zimmermann, J.
Electrost. 21, 151, 1988; T. L. Peck, R. L. Magin, and P. C.
Lauterbur, J. Magn. Reson., Ser. B 108, 114, 1995; A. G. Webb,
Prog. Nucl. Magn. Reson. Spectrosc. 31, 1, 1997; and N. Muller and
A. Jerschow, Proc. Natl. Acad. Sci. U.S.A. 103, 6790, 2006, which
are incorporated by reference herein.
6. Method of Tomographic Imaging
FIG. 8A is a flowchart of an exemplary method 800 of tomographic
imaging. The method 800 begins with an operation 802 of directing
radiation comprising information of a sample from a radiation
source. Next in operation 804 a plurality of one-dimensional
projection scan signals of the sample are generated, each of the
one-dimensional projection scan signals generated from the directed
radiation received by one or more stripe sensor elements at a
distinct relative angle and each of the one or more stripe sensor
elements having a width substantially greater than a thickness.
Finally, in operation 806 a tomographic image of the sample is
derived by combining the plurality of one-dimensional projection
scan signals of the sample with one or more computing devices. The
method 800 may be further modified consistent with the apparatuses
and examples previously described. For example, the method 800 may
be further defined through specific sub-operations for deriving the
tomographic image by combining the plurality of one-dimensional
projection scan signals of the sample.
FIG. 8B is a flowchart of a sub-method 810 for deriving the
tomographic image by combining the plurality of one-dimensional
projection scan signals of the sample. The sub-method 810 begins by
an operation 812 of calculating a Fourier transform of the
plurality of one-dimensional projection scan signals. Next in
operation 814 the Fourier transform is multiplied by a ramp
function in conjugate space. Following this, an inverse
transformation is performed on the multiplied Fourier transform in
operation 816. Finally in operation 818 the inverse transformed
multiplied Fourier transform is integrated over all angles.
This concludes the description including the preferred embodiments
of the present invention. The foregoing description including the
preferred embodiment of the invention has been presented for the
purposes of illustration and description. It is not intended to be
exhaustive or to limit the invention to the precise forms
disclosed. Many modifications and variations are possible within
the scope of the foregoing teachings. Additional variations of the
present invention may be devised without departing from the
inventive concept as set forth in the following claims.
* * * * *